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(5/(x+2)^2+(-4-2*x)*(5*x+8)/(x+2)^4)*exp(-1/(x+2))+(5*x+8)*exp(-1/(x+2))/((x+2)^2*(x+2)^2)
Общий знаменатель (5/(x+2)^2+(-4-2*x)*(5*x+8)/(x+2)^4)*exp(-1/(x+2))+(5*x+8)*exp(-1/(x+2))/((x+2)^2*(x+2)^2)
Решение
Вы ввели
[src]
-1
-1 -----
----- x + 2
/ 5 (-4 - 2*x)*(5*x + 8)\ x + 2 (5*x + 8)*e
|-------- + --------------------|*e + -----------------
| 2 4 | 2 2
\(x + 2) (x + 2) / (x + 2) *(x + 2)
$$\left(\frac{\left(5 x + 8\right) \left(- 2 x - 4\right)}{\left(x + 2\right)^{4}} + \frac{5}{\left(x + 2\right)^{2}}\right) e^{- \frac{1}{x + 2}} + \frac{\left(5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{2} \left(x + 2\right)^{2}}$$
(5/((x + 2)^2) + (-4 - 2*x)*(5*x + 8)/((x + 2)^4))*exp(-1/(x + 2)) + (5*x + 8)*exp(-1/(x + 2))/(((x + 2)^2*(x + 2)^2))
Общее упрощение
[src]
-1
-----
2 + x
(8 + 5*x - (2 + x)*(6 + 5*x))*e
------------------------------------
4
(2 + x)
$$\frac{\left(- \left(x + 2\right) \left(5 x + 6\right) + 5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
(8 + 5*x - (2 + x)*(6 + 5*x))*exp(-1/(2 + x))/(2 + x)^4
Собрать выражение
[src]
-1
-1 -----
----- x + 2
/ 5 (-4 - 2*x)*(8 + 5*x)\ x + 2 (8 + 5*x)*e
|-------- + --------------------|*e + ----------------
| 2 4 | 4
\(2 + x) (2 + x) / (2 + x)
$$\left(\frac{\left(- 2 x - 4\right) \left(5 x + 8\right)}{\left(x + 2\right)^{4}} + \frac{5}{\left(x + 2\right)^{2}}\right) e^{- \frac{1}{x + 2}} + \frac{\left(5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
(5/(2 + x)^2 + (-4 - 2*x)*(8 + 5*x)/(2 + x)^4)*exp(-1/(x + 2)) + (8 + 5*x)*exp(-1/(x + 2))/(2 + x)^4
Тригонометрическая часть
[src]
-1
-----
2 + x
(8 + 5*x - (2 + x)*(6 + 5*x))*e
------------------------------------
4
(2 + x)
$$\frac{\left(- \left(x + 2\right) \left(5 x + 6\right) + 5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
-1
-1 -----
----- 2 + x
/ 5 (-4 - 2*x)*(8 + 5*x)\ 2 + x (8 + 5*x)*e
|-------- + --------------------|*e + ----------------
| 2 4 | 4
\(2 + x) (2 + x) / (2 + x)
$$\left(\frac{\left(- 2 x - 4\right) \left(5 x + 8\right)}{\left(x + 2\right)^{4}} + \frac{5}{\left(x + 2\right)^{2}}\right) e^{- \frac{1}{x + 2}} + \frac{\left(5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
-1 -1
----- -----
/ 4 2 \ 2 + x 2 + x
\5*(2 + x) + (2 + x) *(-4 - 2*x)*(8 + 5*x)/*e (8 + 5*x)*e
--------------------------------------------------- + ----------------
6 4
(2 + x) (2 + x)
$$\frac{\left(5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}} + \frac{\left(\left(- 2 x - 4\right) \left(x + 2\right)^{2} \cdot \left(5 x + 8\right) + 5 \left(x + 2\right)^{4}\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{6}}$$
/ / 1 \ / 1 \\
(8 + 5*x)*|- cosh|-----| + sinh|-----||
/ / 1 \ / 1 \\ / 5 (4 + 2*x)*(8 + 5*x)\ \ \2 + x/ \2 + x//
- |- cosh|-----| + sinh|-----||*|-------- - -------------------| - ---------------------------------------
\ \2 + x/ \2 + x// | 2 4 | 4
\(2 + x) (2 + x) / (2 + x)
$$- \left(\frac{5}{\left(x + 2\right)^{2}} - \frac{\left(2 x + 4\right) \left(5 x + 8\right)}{\left(x + 2\right)^{4}}\right) \left(\sinh{\left(\frac{1}{x + 2} \right)} - \cosh{\left(\frac{1}{x + 2} \right)}\right) - \frac{\left(5 x + 8\right) \left(\sinh{\left(\frac{1}{x + 2} \right)} - \cosh{\left(\frac{1}{x + 2} \right)}\right)}{\left(x + 2\right)^{4}}$$
/ / 1 \ / 1 \\
(8 + 5*x)*|- sinh|-----| + cosh|-----||
/ / 1 \ / 1 \\ / 5 (-4 - 2*x)*(8 + 5*x)\ \ \2 + x/ \2 + x//
|- sinh|-----| + cosh|-----||*|-------- + --------------------| + ---------------------------------------
\ \2 + x/ \2 + x// | 2 4 | 4
\(2 + x) (2 + x) / (2 + x)
$$\left(\frac{\left(- 2 x - 4\right) \left(5 x + 8\right)}{\left(x + 2\right)^{4}} + \frac{5}{\left(x + 2\right)^{2}}\right) \left(- \sinh{\left(\frac{1}{x + 2} \right)} + \cosh{\left(\frac{1}{x + 2} \right)}\right) + \frac{\left(5 x + 8\right) \left(- \sinh{\left(\frac{1}{x + 2} \right)} + \cosh{\left(\frac{1}{x + 2} \right)}\right)}{\left(x + 2\right)^{4}}$$
(-sinh(1/(2 + x)) + cosh(1/(2 + x)))*(5/(2 + x)^2 + (-4 - 2*x)*(8 + 5*x)/(2 + x)^4) + (8 + 5*x)*(-sinh(1/(2 + x)) + cosh(1/(2 + x)))/(2 + x)^4
Степени
[src]
-1
-1 -----
----- 2 + x
/ 5 (-4 - 2*x)*(8 + 5*x)\ 2 + x (8 + 5*x)*e
|-------- + --------------------|*e + ----------------
| 2 4 | 4
\(2 + x) (2 + x) / (2 + x)
$$\left(\frac{\left(- 2 x - 4\right) \left(5 x + 8\right)}{\left(x + 2\right)^{4}} + \frac{5}{\left(x + 2\right)^{2}}\right) e^{- \frac{1}{x + 2}} + \frac{\left(5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
-1
-1 -----
----- x + 2
/ 5 (-4 - 2*x)*(8 + 5*x)\ x + 2 (8 + 5*x)*e
|-------- + --------------------|*e + ----------------
| 2 4 | 4
\(x + 2) (x + 2) / (x + 2)
$$\left(\frac{\left(- 2 x - 4\right) \left(5 x + 8\right)}{\left(x + 2\right)^{4}} + \frac{5}{\left(x + 2\right)^{2}}\right) e^{- \frac{1}{x + 2}} + \frac{\left(5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
(5/(x + 2)^2 + (-4 - 2*x)*(8 + 5*x)/(x + 2)^4)*exp(-1/(x + 2)) + (8 + 5*x)*exp(-1/(x + 2))/(x + 2)^4
Общий знаменатель
[src]
2
-4 - 11*x - 5*x
----------------------------------------------------------------
1 1 1 1 1
----- ----- ----- ----- -----
2 + x 4 2 + x 3 2 + x 2 2 + x 2 + x
16*e + x *e + 8*x *e + 24*x *e + 32*x*e
$$\frac{- 5 x^{2} - 11 x - 4}{x^{4} e^{\frac{1}{x + 2}} + 8 x^{3} e^{\frac{1}{x + 2}} + 24 x^{2} e^{\frac{1}{x + 2}} + 32 x e^{\frac{1}{x + 2}} + 16 e^{\frac{1}{x + 2}}}$$
(-4 - 11*x - 5*x^2)/(16*exp(1/(2 + x)) + x^4*exp(1/(2 + x)) + 8*x^3*exp(1/(2 + x)) + 24*x^2*exp(1/(2 + x)) + 32*x*exp(1/(2 + x)))
Комбинаторика
[src]
-1
-----
/ 2 \ 2 + x
-\4 + 5*x + 11*x/*e
--------------------------
4
(2 + x)
$$- \frac{\left(5 x^{2} + 11 x + 4\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
-(4 + 5*x^2 + 11*x)*exp(-1/(2 + x))/(2 + x)^4
Объединение рациональных выражений
[src]
-1
-----
/ 2 \ 2 + x
\8 + 5*x + 5*(2 + x) + 2*(-2 - x)*(8 + 5*x)/*e
----------------------------------------------------
4
(2 + x)
$$\frac{\left(2 \left(- x - 2\right) \left(5 x + 8\right) + 5 \left(x + 2\right)^{2} + 5 x + 8\right) e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
(8 + 5*x + 5*(2 + x)^2 + 2*(-2 - x)*(8 + 5*x))*exp(-1/(2 + x))/(2 + x)^4
Численный ответ
[src]
(1.25/(1 + 0.5*x)^2 + 0.0625*(8.0 + 5.0*x)*(-4.0 - 2.0*x)/(1 + 0.5*x)^4)*exp(-1/(x + 2)) + 0.0625*(8.0 + 5.0*x)*exp(-1/(x + 2))/(1 + 0.5*x)^4
(1.25/(1 + 0.5*x)^2 + 0.0625*(8.0 + 5.0*x)*(-4.0 - 2.0*x)/(1 + 0.5*x)^4)*exp(-1/(x + 2)) + 0.0625*(8.0 + 5.0*x)*exp(-1/(x + 2))/(1 + 0.5*x)^4
Рациональный знаменатель
[src]
-1 -1 -1 -1
----- ----- ----- -----
2 + x 2 + x 2 + x 2 2 + x
24*e 5*e 31*x*e 10*x *e
- --------- + -------- - ----------- - ------------
4 2 4 4
(2 + x) (2 + x) (2 + x) (2 + x)
$$- \frac{10 x^{2} e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}} + \frac{5 e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{2}} - \frac{31 x e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}} - \frac{24 e^{- \frac{1}{x + 2}}}{\left(x + 2\right)^{4}}$$
/ 1 1 \ -2
| ----- -----| -----
| 4 / 4 2 \ x + 2 6 x + 2| x + 2
\(2 + x) *\5*(2 + x) + (2 + x) *(-4 - 2*x)*(8 + 5*x)/*e + (2 + x) *(8 + 5*x)*e /*e
-------------------------------------------------------------------------------------------------
10
(2 + x)
$$\frac{\left(\left(x + 2\right)^{6} \cdot \left(5 x + 8\right) e^{\frac{1}{x + 2}} + \left(x + 2\right)^{4} \left(\left(- 2 x - 4\right) \left(x + 2\right)^{2} \cdot \left(5 x + 8\right) + 5 \left(x + 2\right)^{4}\right) e^{\frac{1}{x + 2}}\right) e^{- \frac{2}{x + 2}}}{\left(x + 2\right)^{10}}$$
((2 + x)^4*(5*(2 + x)^4 + (2 + x)^2*(-4 - 2*x)*(8 + 5*x))*exp(1/(x + 2)) + (2 + x)^6*(8 + 5*x)*exp(1/(x + 2)))*exp(-2/(x + 2))/(2 + x)^10